The question of whether someone who is mixed-race is, in fact, "black" has been the subject of much discussion since Barack Obama began to be taken seriously as a contender for president. For those, like myself, who are mixed-race and had settled into our black identity a long time ago, the debate has been sometimes uncomfortable. While for some it was a moment for personal expression, for others the separation of "mixed race" from "black" is anathema.

It has been a debate that engaged this country more than the US. The proportion of mixed-race citizens, whose numbers famously include the Formula One racing driver Lewis Hamilton, is rising much faster here, and previously straightforward ethnic categories are being questioned by younger generations. With 63% of black Caribbean men born in the UK in mixed relationships, it is a trend that is set to continue.

It's useful to see how the next US president, a master of racial nuance, handles this issue. Obama celebrates, even jokes about, his own diverse background. The love of his white American family pours from his biography, alongside his deep connection to his Kenyan relatives. But there is no question that the world's most famous mixed-race man identifies himself as, among other things, a black man. His view, if you have travelled a similar path and reached the same conclusion, is a powerful affirmation.

Frequently in Dreams From My Father, Obama confidently refers to himself as a "black man". The book's account of a student named Joyce is strikingly familiar to any of us who have been in his situation. She shakes her head when the young Obama asks if she is coming to the Black Students' Association meeting. "I'm not black, I'm multiracial," she insists, and after relating her mixed origins she laments: "Why should I have to choose between them?" It is black people, she says, not white, who are forcing an uncomfortable "choice". Obama is not persuaded. His empathetic criticism of her perspective is followed by his telling description of her as one of the "black" students. How he would define her seems clear.

Why has he reached that position? For me, it is because he recognises the fundamental error of those who try to assert that "mixed-race" is separate from "black". They have misunderstood that the term "black" has always included mixed-race and lighter skinned people of African heritage. By its very definition, "black" has not overlooked us, but embraced us.

Discussions about whether mixed-race people are "black" often focus on racism's all-encompassing antipathy towards darker people; or the infamous "one drop" rule that categorised all persons with some African blood as forever second class. We were all grouped together. A less racist society, the argument goes, would have recognised us as different, and it should do so now.

The problem with that well-meaning approach is that it is both inaccurate and reactionary. It was the most racist societies that highlighted such distinctions and, to our collective credit, we moved on. The American South proudly divided slaves into "negroes", "mulattos", "quadroons" and "octoroons". Apartheid South Africa, also differentiated between "black" and "coloured". It is ironic when seemingly progressive commentators want to return to that position.

In deliberate contrast, "black" did not make distinctions based on racial purity. There were two key reasons the term became ubiquitous in the 1960s. First, it was unifying. African-Americans, like Caribbeans, are a physically diverse, but culturally connected people. So to describe all those of African lineage with one label, spoke to that shared cultural heritage. Second, it was liberating. The phenomenon of everyone from "negroes" to "quadroons" choosing to redefine themselves as "black", regardless of skin tone or hair texture, consciously subverted a discredited history of oppression. The closeness to white ancestry was no longer the defining source of our identity. "Black" was virtually revolutionary.

Once the genesis of the term is understood, the fallacy that "mixed race" can or should be separated from "black" is exposed. By definition, "black" includes mixed-race; to assert otherwise would mean changing what "black" means. And, if so, are we supposed to invent a new term for a group of "black" people who are racially "pure"? No such divisive concept has been part of our culture in recent memory. Obama also describes himself as "African-American". Certainly, there are strong arguments that the term "African" should now be embraced in preference to the term "black", but that is a different debate. What it shows is how comfortably he wears the complexity of who he is. There is nothing limiting about his version of blackness because it connects to a world view: "Our trials and triumphs became at once unique and universal, black and more than black...".

Around the world, particularly in the UK, Obama has not merely raised the issue as to whether a person who is mixed-race can be black - if anything, he has settled it. The real beauty is his understanding that different identities can confidently coexist in the same person. His black identity is not hostile towards, or exclusive of, his white relatives. Perhaps, having resolved that issue, we can now begin to focus on the important business of what the first black president does, rather than continuing to agonise over what he is.

Social and ethnic demographics in the UK will shift dramatically in our lifetimes, as today's survey shows. If we embrace our own multiple identities and enjoy who we are, instead of arguing over what we are not, we can face the future with more confidence. That is why I, and many others like me, remain unapologetically and happily African, Caribbean, British, European, mixed-race and, of course, black.